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PROPERTIES OF GEODETIC INDEPENDENCE POLYNOMIALS
Keywords:
geodetic independent set, geodetic independent polynomial.DOI:
https://doi.org/10.17654/0974165824007Abstract
Let $G$ be a simple connected graph. Then the geodetic independence polynomial of $G$, denoted by $g(G; x)$, is the polynomial whose coefficients correspond to the number of geodetic independent subsets of $V(G)$. In this paper, we obtain some properties of geodetic independence polynomial of a graph. Moreover, we characterize the geodetic independent sets of a complete graph.
Received: November 29, 2023
Accepted: January 3, 2024
References
R. G. Artes, Jr. and R. A. Rasid, Balanced biclique polynomial of graphs, Global J. Pure Appl. Math. 12(5) (2016), 4427-4433.
R. G. Artes, Jr., N. H. R. Mohammad, A. A. Laja and N. H. M. Hassan, From graphs to polynomial rings: star polynomial representation of graphs, Advances and Applications in Discrete Mathematics 37 (2023), 67-76.
https://doi.org/10.17654/0974165823012.
R. G. Artes, Jr., N. H. R. Mohammad, Z. H. Dael and H. B. Copel, Star polynomial of the corona of graphs, Advances and Applications in Discrete Mathematics 39(1) (2023), 81-87. https://doi.org/10.17654/0974165823037.
R. G. Artes, Jr. and R. A. Rasid, Combinatorial approach in counting the balanced bicliques in the join and corona of graphs, Journal of Ultra Scientist of Physical Sciences 29(5) (2017), 192-195.
R. G. Artes, Jr., J. I. C. Salim, R. A. Rasid, J. I. Edubos and B. J. Amiruddin, Geodetic closure polynomial of graphs, International Journal of Mathematics and Computer Science 19(2) (2024), 439-443.
J. A. Bondy and U. S. R. Murty, Graph Theory and Related Topics, Academic Press, New York, 1979.
J. Ellis-Monaghan and J. Merino, Graph Polynomials and their Applications II: Interrelations and Interpretations, Birkhauser, Boston, 2011.
F. Harary, Graph Theory, CRC Press, Boca Raton, 2018.
C. Hoede and X. Li, Clique polynomials and independent set polynomials of graphs, Discrete Math. 125 (1994), 219-228.
L. S. Laja and R. G. Artes, Jr., Zeros of convex subgraph polynomials, Appl. Math. Sci. 8(59) (2014), 2917-2923.
http://dx.doi.org/10.12988/ams.2014.44285.
L. S. Laja and R. G. Artes, Jr., Convex subgraph polynomials of the join and the composition of graphs, International Journal of Mathematical Analysis 10(11) (2016), 515-529. http://dx.doi.org/10.12988/ijma.2016.512296.
R. E. Madalim, R. G. Eballe, A. H. Arajaini and R. G. Artes, Jr., Induced cycle polynomial of a graph, Advances and Applications in Discrete Mathematics 38(1) (2023), 83-94. https://doi.org/10.17654/0974165823020.
C. A. Villarta, R. G. Eballe and R. G. Artes, Jr., Induced path polynomial of graphs, Advances and Applications in Discrete Mathematics 39(2) (2023), 183-190. https://doi.org/10.17654/0974165823045.
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